Some strategies that work when operating with whole numbers hold up when working with decimals or fractions; some do not. In Operation Sense, students:
- Use mostly mental math and estimation skills to reason about operations with rational numbers
- Use diagrams, number lines, and models to visualize situations in which rational numbers are added, subtracted, multiplied, and divided
- Begin to formulate a sense of how results differ when, for instance, they multiply by a fraction rather than a whole number
- Become comfortable with decimal-fraction equivalencies so they can use the form that best fits a problem or their own preferred strategies
As students solve problems taken from everyday life contexts, they connect operations with fractions, decimals, and percents to related math content, in particular geometry and data.
The work begins with consideration of operations with benchmark rational numbers then moves to 'messier' numbers, like 7/16.
Students are always asked to consider: Does that answer make sense? Algorithms emerge from students' own reasoning and practices, so they remain robust long after students leave the classroom. This is not a book about copying steps outlined at the top of the page; it is a book that helps students understand phenomena that fly in the face of what people have come to expect when operating on whole numbers. For example, one can multiply to get an answer smaller than the factors (e.g., 1/2 • 1/2 =1/4), or one can divide by a decimal and get a quotient larger than the dividend. Students learn to calculate; but they also learn to recognize reasonable answers, so if they hit the wrong calculator buttons or the right buttons in the wrong sequence, they know it.
The Teacher Book is an essential component of the EMPower program. It is designed to be used in conjunction with the Student Book. The Teacher Book includes:
- Suggestions for facilitating class discussions
- Open-ended questions designed to keep the math on track
- Math Background sections to help teachers deepen their understanding of a concept
- Lesson in Action sections with examples of student work and comments that illuminate the underlying mathematics
- Examples from the authors' and pilot teachers' classroom experiences